A routing number is a 9 digit code for identifying a financial institution for the purpose of routing of checks (cheques), fund transfers, direct deposits, e-payments, online payments, and other payments to the correct bank branch.

Routing numbers are also known as banking routing numbers, routing transit numbers, RTNs, ABA numbers, and sometimes SWIFT codes (although these are quite different from routing numbers as SWIFT codes are solely used for international wire transfers while routing numbers are used for domestic transfers).

Routing numbers differ for checking and savings accounts, prepaid cards, IRAs, lines of credit, and wire transfers.
All banks usually have separate routing numbers for each of the states in the US.

You can look for the routing number on the check (cheque book) issued by your bank or can search this website for free.

ABA Routing Number: Routing numbers are also referred to as "Check Routing Numbers", "ABA Numbers", or "Routing Transit Numbers" (RTN). The ABA routing number is a 9-digit identification number assigned to financial institutions by The American Bankers Association (ABA). This number identifies the financial institution upon which a payment is drawn. Routing numbers may differ depending on where your account was opened and the type of transaction made.
Each routing number is unique to a particular bank, large banks may have more than one routing number for different states.

ACH Routing Number: ACH Routing Number stands for Automated Clearing House (ACH). This routing number is used for electronic financial transactions in the United States. ACH helps to improves payment processing efficiency and accuracy, and reduce expenses. Banks offer ACH services for businesses who want to collect funds and make payments electronically in batches through the national ACH network. ACH routing number is a nine digit number.
The first four digits identify the Federal Reserve district where the bank is located. The next four numbers identify the specific bank. The last number is called as a check digit number which is a confirmation number. ACH Routing Numbers are used for direct deposit of payroll, dividends, annuities, monthly payments and collections, federal and state tax payments etc.

Fedwire Routing Number: Fedwire Transfer service is the most expedient method for transferring funds between business account and other bank accounts.
It is used for domestic or international transactions in which no cash or check exchange is involved, but the account balance is directly debited electronically and the funds are transferred to another account in real time. To complete a wire transfer, the sender must provide his bank name and account number of the recipient, the receiving account number, the city and state of the receiving bank and the bank's routing number.